Finite Group Databasebeta

← C2×#11755022 #14480328

Subgroups — C2×#11755022 #14480328

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×D5×#67C211yesmaximal, characteristic, complemented
3C2×#91827C211yesmaximal, characteristic, complemented
4C2×C5×#937C211yesmaximal, characteristic, complemented
5C2×C3×#4083C211yesmaximal, characteristic, complemented
6C2×#91568C211yesmaximal, characteristic, complemented
7C2×#91563C211yesmaximal, characteristic, complemented
8C2×#91557C211yesmaximal, characteristic, complemented
9C2×#91555C211yesmaximal, characteristic, complemented
10C2×#91548C211yesmaximal, characteristic, complemented
11C2×#91533C211yesmaximal, characteristic, complemented
12#11755022C2116yesmaximal, direct product factor
13C2×#91473C211yesmaximal, characteristic, complemented
14C2×#91461C211yesmaximal, characteristic, complemented
15C2×#91457C211yesmaximal, characteristic, complemented
16C2×#91414C211yesmaximal, characteristic, complemented
17C2×#65923—31nomaximal, Hall
18C24×C5×D3C2211yescharacteristic, complemented
19C24×C3×D5C2211yescharacteristic, complemented
20C23×D3×D5C2211yescharacteristic
21C22×C3×C5×D4C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic, complemented
23C22×#1220C2211yescharacteristic, complemented
24C22×C4×D15C2211yescharacteristic, complemented
25C22×C5×#67C2211yescharacteristic
26C22×C5×#67C2211yescharacteristic, complemented
27C22×C3×C22⋊D5C2211yescharacteristic
28C22×C3×C22⋊D5C2211yescharacteristic, complemented
29C2×D3×C22⋊D5—28no—
30C2×D3×C22⋊D5C2218yescomplemented
31C2×D5×#67—28no—
32C2×D5×#67C2218yescomplemented
33C22×#1203C2211yescharacteristic, complemented
34C22×#1202C2211yescharacteristic, complemented
35C22×#1201C2211yescharacteristic
36C22×#1201C2211yescharacteristic
37C22×#1201C2211yescharacteristic, complemented
38C22×#1200C2211yescharacteristic, complemented
39C22×D3×Dic5C2211yescharacteristic, complemented
40C22×D5×Dic3C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42C2×#6719C2211yescharacteristic, complemented
43#91827C2218yescomplemented
44C2×C4⋊Dic15C2211yescharacteristic, complemented
45C2×C5×#217C2211yescharacteristic, complemented
46C5×#937C2218yescomplemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C3×#4083C2218yescomplemented
51C2×C3×#685C2211yescharacteristic, complemented
52C2×C3×#685C2211yescharacteristic, complemented
53#91568C2218yescomplemented
54#91563C2218yescomplemented
55#91557C2218yescomplemented
56#91555C2218yescomplemented
57#91548C2218yescomplemented
58C2×Dic3⋊Dic5C2211yescharacteristic, complemented
59C2×#6669C2211yescharacteristic, complemented
60C2×#6668C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
63C2×#6665C2211yescharacteristic, complemented
64C2×#6665C2211yescharacteristic, complemented
65#91533C2218yescomplemented
66#91473C2218yescomplemented
67#91461C2218yescomplemented
68#91457C2218yescomplemented
69#91414C2218yescomplemented
70C2×#5589—51nomaximal, Hall
71C23×C22⋊D5—31no—
72C22×D4×D5—31no—
73C2×C5×#120—31no—
74C2×#4099—31no—
75C2×#4084—31no—
76C2×#4084—31no—
77C2×#4083—31no—
78C2×#4083D311yescharacteristic, complemented
79C2×#4081—31no—
80#65923—316no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4030—31no—
84C2×#4029—31no—
85C2×#4029—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3—24no—
91C23×C5×D3—42no—
92C23×C5×D3—42no—
93C23×C5×D3C2311yescharacteristic
94C23×C5×D3C2311yescharacteristic
95C23×C5×D3C2314yescomplemented
96C23×C3×D5—24no—
97C23×C3×D5—42no—
98C23×C3×D5—42no—
99C23×C3×D5C2311yescharacteristic
100C23×C3×D5C2311yescharacteristic
101C23×C3×D5C2314yescomplemented
102C22×D3×D5—42no—
103C22×D3×D5—42no—
104C22×D3×D5D418yescomplemented
105C22×D3×D5C2314yes—
106C2×C3×C5×D4—42no—
107C2×C3×C5×D4C2314yescomplemented
108C22×C3×C4×C5C2311yescharacteristic
109C2×#1220—24no—
110C2×#1220—24no—
111C2×#1220C2314yescomplemented
112C2×#1220C2314yescomplemented
113C22×Dic15C2311yescharacteristic
114C22×Dic15C2311yescharacteristic
115C22×Dic15C2311yescharacteristic
116C2×C4×D15—42no—
117C2×C4×D15C2314yescomplemented
118C2×C5×#67—24no—
119C2×C5×#67—42no—
120C2×C5×#67C2314yes—
121C2×C5×#67C2314yescomplemented
122C22×C5×Dic3C2311yescharacteristic
123C22×C5×Dic3C2311yescharacteristic
124C2×C3×C22⋊D5—24no—
125C2×C3×C22⋊D5—42no—
126C2×C3×C22⋊D5C2314yes—
127C2×C3×C22⋊D5C2314yescomplemented
128C22×C3×Dic5C2311yescharacteristic
129C22×C3×Dic5C2311yescharacteristic
130D3×C22⋊D5—232no—
131D5×#67—232no—
132C2×#1203—24no—
133C2×#1203C2314yescomplemented
134C2×#1202—24no—
135C2×#1202C2314yescomplemented
136C2×#1201—24no—
137C2×#1201—24no—
138C2×#1201—42no—
139C2×#1201C2314yes—
140C2×#1201C2314yes—
141C2×#1201C2314yescomplemented
142C2×#1200—42no—
143C2×#1200C2314yescomplemented
144C2×D3×Dic5—24no—
145C2×D3×Dic5C2314yescomplemented
146C2×D5×Dic3—24no—
147C2×D5×Dic3C2314yescomplemented
148#6719C2314yescomplemented
149#6719C2314yescomplemented
150C4⋊Dic15C2314yescomplemented
151C5×#217C2314yescomplemented
152C5×(C2×D3)⋊C4C2314yescomplemented
153C5×(C2×D3)⋊C4C2314yescomplemented
154C3×C22⋊Dic5C2314yescomplemented
155C3×#685C2314yescomplemented
156C3×#685C2314yescomplemented
157Dic3⋊Dic5C2314yescomplemented
158#6669C2314yescomplemented
159#6668C2314yescomplemented
160(C2×D3)⋊Dic5C2314yescomplemented
161(C2×D3)⋊Dic5C2314yescomplemented
162#6665C2314yescomplemented
163#6665C2314yescomplemented
164C23×#67—51no—
165C22×D3×D4—51no—
166C2×C3×#120—51no—
167C2×#953—51no—
168C2×#938—51no—
169C2×#938—51no—
170C2×#937—51no—
171C2×#937D511yescharacteristic, complemented
172C2×#935—51no—
173#5589—516no—
174C2×#886—51no—
175C2×#884—51no—
176C2×#884—51no—
177C2×#883—51no—
178C2×#883—51no—
179C2×D3×C22⋊C4—51no—
180C25×C5—31no—
181C24×D5—31no—
182C24×D5C2×D311yescharacteristic, complemented
183C22×C5×D4—31no—
184C22×C5×D4—31no—
185C22×C5×D4C2×D311yescharacteristic, complemented
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—31no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5—38no—
192C22×C22⋊D5—31no—
193C22×C22⋊D5—68no—
194C22×C22⋊D5C2×D311yescharacteristic
195C22×C22⋊D5C2×D311yescharacteristic, complemented
196C23×Dic5—31no—
197C2×D4×D5—38no—
198C2×D4×D5—68no—
199C22×D20—31no—
200C22×C4×D5—31no—
201C22×C4×D5—31no—
202C22×C4×D5—31no—
203C5×#120—38no—
204C2×C5×C22⋊C4—31no—
205C2×C5×C22⋊C4—31no—
206C2×C5×C22⋊C4—31no—
207#4099—38no—
208C2×C22⋊Dic5—31no—
209C2×C22⋊Dic5—31no—
210C2×C22⋊Dic5—31no—
211C2×C22⋊Dic5—31no—
212C2×C22⋊Dic5C2×D311yescharacteristic, complemented
213#4084—38no—
214#4084—38no—
215#4083—38no—
216#4083C2×D318yescomplemented
217#4081—38no—
218C2×#685—31no—
219C2×#685—31no—
220C2×#685C2×D311yescharacteristic, complemented
221C2×#685C2×D311yescharacteristic, complemented
222C2×C4⋊Dic5—31no—
223C2×C4⋊Dic5—31no—
224C2×#683—31no—
225C2×#683—31no—
226#4032—38no—
227#4030—38no—
228#4030—38no—
229#4029—38no—
230#4029—38no—
231D5×C22⋊C4—38no—
232C2×#534—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5—22no—
237C23×C3×C5—22no—
238C23×C3×C5—22no—
239C23×C3×C5C2412yes—
240C23×C3×C5C2412yes—
241C23×C3×C5C2411yescharacteristic
242C22×D15—22no—
243C22×D15—22no—
244C22×D15C2×D414yes—
245C22×D15C2412yes—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3—22no—
250C22×C5×D3—22no—
251C22×C5×D3—28no—
252C22×C5×D3—44no—
253C22×C5×D3—44no—
254C22×C5×D3—416no—
255C22×C5×D3C2×D414yes—
256C22×C5×D3C2412yes—
257C22×C5×D3C2412yes—
258C22×C3×D5—22no—
259C22×C3×D5—22no—
260C22×C3×D5—22no—
261C22×C3×D5—22no—
262C22×C3×D5—22no—
263C22×C3×D5—28no—
264C22×C3×D5—44no—
265C22×C3×D5—44no—
266C22×C3×D5—416no—
267C22×C3×D5C2×D414yes—
268C22×C3×D5C2412yes—
269C22×C3×D5C2412yes—
270C2×D3×D5—416no—
271C2×D3×D5—44no—
272C2×D3×D5—44no—
273C2×D3×D5C2×D4116yescomplemented
274C3×C5×D4—44no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5C2412yes—
277#1220—28no—
278#1220—28no—
279C2×Dic15—22no—
280C2×Dic15—22no—
281C2×Dic15—22no—
282C2×Dic15C2412yes—
283C2×Dic15C2412yes—
284C2×Dic15C2412yes—
285C4×D15—44no—
286C5×#67—28no—
287C5×#67—44no—
288C2×C5×Dic3—22no—
289C2×C5×Dic3—22no—
290C2×C5×Dic3C2412yes—
291C2×C5×Dic3C2412yes—
292C3×C22⋊D5—28no—
293C3×C22⋊D5—44no—
294C2×C3×Dic5—22no—
295C2×C3×Dic5—22no—
296C2×C3×Dic5C2412yes—
297C2×C3×Dic5C2412yes—
298#1203—28no—
299#1202—28no—
300#1201—28no—
301#1201—28no—
302#1201—44no—
303#1200—44no—
304D3×Dic5—28no—
305D5×Dic3—28no—
306C25×C3—51no—
307C24×D3—51no—
308C24×D3C2×D511yescharacteristic, complemented
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4C2×D511yescharacteristic, complemented
312C22×#67—51no—
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—51no—
316C22×#67—51no—
317C22×#67—58no—
318C22×#67—51no—
319C22×#67—108no—
320C22×#67C2×D511yescharacteristic
321C22×#67C2×D511yescharacteristic, complemented
322C23×Dic3—51no—
323C2×D3×D4—58no—
324C2×D3×D4—108no—
325C22×D12—51no—
326C22×C4×D3—51no—
327C22×C4×D3—51no—
328C22×C4×D3—51no—
329C3×#120—58no—
330C2×C3×C22⋊C4—51no—
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333#953—58no—
334C2×#217—51no—
335C2×#217—51no—
336C2×#217—51no—
337C2×#217—51no—
338C2×#217C2×D511yescharacteristic, complemented
339#938—58no—
340#938—58no—
341#937—58no—
342#937C2×D518yescomplemented
343#935—58no—
344C2×(C2×D3)⋊C4—51no—
345C2×(C2×D3)⋊C4—51no—
346C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
347C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
348C2×C4⋊Dic3—51no—
349C2×C4⋊Dic3—51no—
350C2×Dic3⋊C4—51no—
351C2×Dic3⋊C4—51no—
352#886—58no—
353#884—58no—
354#884—58no—
355#883—58no—
356#883—58no—
357D3×C22⋊C4—58no—
358C24×C5—31no—
359C24×C5—31no—
360C24×C5—34no—
361C24×C5—64no—
362C24×C5—122no—
363C24×C5—122no—
364C24×C5C22×D311yescharacteristic
365C24×C5C22×D311yescharacteristic
366C23×D5—24no—
367C23×D5—31no—
368C23×D5—38no—
369C23×D5—34no—
370C23×D5—42no—
371C23×D5—42no—
372C23×D5—122no—
373C23×D5—122no—
374C23×D5C22×D311yescharacteristic
375C23×D5C22×D311yescharacteristic
376C23×D5C22×D314yescomplemented
377C2×C5×D4—34no—
378C2×C5×D4—34no—
379C2×C5×D4—42no—
380C2×C5×D4—64no—
381C2×C5×D4—122no—
382C2×C5×D4C22×D314yescomplemented
383C22×C4×C5—31no—
384C22×C4×C5—31no—
385C22×C4×C5C22×D311yescharacteristic
386C2×C22⋊D5—24no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—34no—
390C2×C22⋊D5—34no—
391C2×C22⋊D5—34no—
392C2×C22⋊D5—34no—
393C2×C22⋊D5—42no—
394C2×C22⋊D5—64no—
395C2×C22⋊D5—632no—
396C2×C22⋊D5—64no—
397C2×C22⋊D5—64no—
398C2×C22⋊D5—64no—
399C2×C22⋊D5—64no—
400C2×C22⋊D5—122no—
401C2×C22⋊D5C22×D314yes—
402C2×C22⋊D5C22×D314yescomplemented
403C22×Dic5—31no—
404C22×Dic5—31no—
405C22×Dic5—31no—
406C22×Dic5—34no—
407C22×Dic5—64no—
408C22×Dic5C22×D311yescharacteristic
409C22×Dic5C22×D311yescharacteristic
410D4×D5—632no—
411C2×D20—34no—
412C2×D20—64no—
413C2×C4×D5—34no—
414C2×C4×D5—34no—
415C2×C4×D5—34no—
416C2×C4×D5—64no—
417C2×C4×D5—122no—
418C2×C4×D5—122no—
419C5×C22⋊C4—34no—
420C5×C22⋊C4—34no—
421C5×C22⋊C4—34no—
422C22⋊Dic5—34no—
423C22⋊Dic5—34no—
424C22⋊Dic5—34no—
425C22⋊Dic5—34no—
426C22⋊Dic5C22×D314yescomplemented
427#685—34no—
428#685—34no—
429#685C22×D314yescomplemented
430#685C22×D314yescomplemented
431C4⋊Dic5—34no—
432C4⋊Dic5—34no—
433#683—34no—
434#683—34no—
435C23×D4—151no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—151no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#121—151no—
446C2×#120—31no—
447C2×#120—51no—
448C2×#120—151no—
449C2×#120—151no—
450C22×C22⋊C4—151no—
451C22×C3×C5—22no—
452C22×C3×C5—22no—
453C22×C3×C5—22no—
454C22×C3×C5—22no—
455C22×C3×C5—22no—
456C22×C3×C5—22no—
457C22×C3×C5—44no—
458C22×C3×C5—44no—
459C22×C3×C5C22×D412yes—
460C22×C3×C5H(5,𝔽2)12yes—
461C22×C3×C5H(5,𝔽2)12yes—
462C22×C3×C5C2511yescharacteristic
463C2×D15—28no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15C22×D414yes—
467C2×C5×D3—28no—
468C2×C5×D3—22no—
469C2×C5×D3—22no—
470C2×C5×D3—22no—
471C2×C5×D3—22no—
472C2×C5×D3—22no—
473C2×C5×D3—416no—
474C2×C5×D3—44no—
475C2×C5×D3C22×D414yes—
476C2×C3×D5—28no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—22no—
481C2×C3×D5—22no—
482C2×C3×D5—416no—
483C2×C3×D5—44no—
484C2×C3×D5C22×D414yes—
485D3×D5—416no—
486C3×C4×C5—22no—
487Dic15—22no—
488Dic15—22no—
489Dic15—22no—
490C3×Dic5—22no—
491C3×Dic5—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3—51no—
496C24×C3—54no—
497C24×C3—104no—
498C24×C3—202no—
499C24×C3—202no—
500C24×C3C22×D511yescharacteristic
501C24×C3C22×D511yescharacteristic
502C23×D3—24no—
503C23×D3—42no—
504C23×D3—42no—
505C23×D3—51no—
506C23×D3—58no—
507C23×D3—54no—
508C23×D3—202no—
509C23×D3—202no—
510C23×D3C22×D511yescharacteristic
511C23×D3C22×D511yescharacteristic
512C23×D3C22×D514yescomplemented
513C2×C3×D4—42no—
514C2×C3×D4—54no—
515C2×C3×D4—54no—
516C2×C3×D4—104no—
517C2×C3×D4—202no—
518C2×C3×D4C22×D514yescomplemented
519C22×C3×C4—51no—
520C22×C3×C4—51no—
521C22×C3×C4C22×D511yescharacteristic
522C2×#67—24no—
523C2×#67—42no—
524C2×#67—54no—
525C2×#67—54no—
526C2×#67—54no—
527C2×#67—54no—
528C2×#67—54no—
529C2×#67—54no—
530C2×#67—104no—
531C2×#67—1032no—
532C2×#67—104no—
533C2×#67—104no—
534C2×#67—104no—
535C2×#67—104no—
536C2×#67—202no—
537C2×#67C22×D514yes—
538C2×#67C22×D514yescomplemented
539C22×Dic3—51no—
540C22×Dic3—51no—
541C22×Dic3—51no—
542C22×Dic3—54no—
543C22×Dic3—104no—
544C22×Dic3C22×D511yescharacteristic
545C22×Dic3C22×D511yescharacteristic
546D3×D4—1032no—
547C2×D12—54no—
548C2×D12—104no—
549C2×C4×D3—54no—
550C2×C4×D3—54no—
551C2×C4×D3—54no—
552C2×C4×D3—104no—
553C2×C4×D3—202no—
554C2×C4×D3—202no—
555C3×C22⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4—54no—
558#217—54no—
559#217—54no—
560#217—54no—
561#217—54no—
562#217C22×D514yescomplemented
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4—54no—
565(C2×D3)⋊C4C22×D514yescomplemented
566(C2×D3)⋊C4C22×D514yescomplemented
567C4⋊Dic3—54no—
568C4⋊Dic3—54no—
569Dic3⋊C4—54no—
570Dic3⋊C4—54no—
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—22no—
575C23×C5—22no—
576C23×C5—22no—
577C23×C5—34no—
578C23×C5—32no—
579C23×C5—32no—
580C23×C5—68no—
581C23×C5—62no—
582C23×C5—62no—
583C23×C5—62no—
584C23×C5—62no—
585C23×C5—62no—
586C23×C5—124no—
587C23×C5—124no—
588C23×C5—1216no—
589C23×C5C23×D312yes—
590C23×C5C23×D312yes—
591C23×C5C23×D311yescharacteristic
592C22×D5—22no—
593C22×D5—22no—
594C22×D5—22no—
595C22×D5—22no—
596C22×D5—22no—
597C22×D5—28no—
598C22×D5—34no—
599C22×D5—32no—
600C22×D5—316no—
601C22×D5—44no—
602C22×D5—44no—
603C22×D5—416no—
604C22×D5—62no—
605C22×D5—62no—
606C22×D5—124no—
607C22×D5—124no—
608C22×D5—1216no—
609C22×D5D3×D414yes—
610C22×D5C23×D312yes—
611C22×D5C23×D312yes—
612C5×D4—44no—
613C5×D4—68no—
614C5×D4—124no—
615C2×C4×C5—22no—
616C2×C4×C5—32no—
617C2×C4×C5—32no—
618C2×C4×C5—62no—
619C2×C4×C5—62no—
620C2×C4×C5C23×D312yes—
621C22⋊D5—28no—
622C22⋊D5—44no—
623C22⋊D5—68no—
624C22⋊D5—68no—
625C22⋊D5—68no—
626C22⋊D5—68no—
627C22⋊D5—68no—
628C22⋊D5—124no—
629C2×Dic5—22no—
630C2×Dic5—22no—
631C2×Dic5—32no—
632C2×Dic5—32no—
633C2×Dic5—32no—
634C2×Dic5—68no—
635C2×Dic5—62no—
636C2×Dic5—62no—
637C2×Dic5—62no—
638C2×Dic5C23×D312yes—
639C2×Dic5C23×D312yes—
640D20—68no—
641C4×D5—68no—
642C4×D5—124no—
643C4×D5—124no—
644C25—31no—
645C25—51no—
646C25—151no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—151no—
652C22×D4—151no—
653C22×D4—158no—
654C22×D4—158no—
655C22×D4—151no—
656C22×D4—151no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—308no—
661C22×D4—308no—
662C22×D4D3×D511yescharacteristic, complemented
663C23×C4—151no—
664C23×C4—151no—
665C23×C4—151no—
666C23×C4—151no—
667#123—158no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—158no—
672#121—158no—
673#121—158no—
674#121—158no—
675#120—38no—
676#120—58no—
677#120—158no—
678#120—158no—
679C2×C4⋊C4—151no—
680C2×C4⋊C4—151no—
681C2×C4⋊C4—151no—
682C2×C4⋊C4—151no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—31no—
686C2×C22⋊C4—51no—
687C2×C22⋊C4—51no—
688C2×C22⋊C4—51no—
689C2×C22⋊C4—158no—
690C2×C22⋊C4—151no—
691C2×C22⋊C4—151no—
692C2×C22⋊C4—151no—
693C2×C22⋊C4—151no—
694C2×C22⋊C4—151no—
695C2×C22⋊C4—151no—
696C2×C3×C5—42no—
697C2×C3×C5—42no—
698C2×C3×C5#53414yescomplemented
699C2×C3×C5C23×D411yescharacteristic
700C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
701C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
702D15—24no—
703C3×D5—24no—
704C3×D5—42no—
705C5×D3—24no—
706C5×D3—42no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—22no—
711C23×C3—22no—
712C23×C3—22no—
713C23×C3—54no—
714C23×C3—52no—
715C23×C3—52no—
716C23×C3—108no—
717C23×C3—102no—
718C23×C3—102no—
719C23×C3—102no—
720C23×C3—102no—
721C23×C3—102no—
722C23×C3—204no—
723C23×C3—204no—
724C23×C3—2016no—
725C23×C3C23×D512yes—
726C23×C3C23×D512yes—
727C23×C3C23×D511yescharacteristic
728C22×D3—22no—
729C22×D3—22no—
730C22×D3—22no—
731C22×D3—22no—
732C22×D3—22no—
733C22×D3—28no—
734C22×D3—44no—
735C22×D3—44no—
736C22×D3—416no—
737C22×D3—54no—
738C22×D3—52no—
739C22×D3—516no—
740C22×D3—102no—
741C22×D3—102no—
742C22×D3—2016no—
743C22×D3—204no—
744C22×D3—204no—
745C22×D3D4×D514yes—
746C22×D3C23×D512yes—
747C22×D3C23×D512yes—
748C3×D4—44no—
749C3×D4—108no—
750C3×D4—204no—
751C2×C3×C4—22no—
752C2×C3×C4—52no—
753C2×C3×C4—52no—
754C2×C3×C4—102no—
755C2×C3×C4—102no—
756C2×C3×C4C23×D512yes—
757#67—28no—
758#67—44no—
759#67—108no—
760#67—108no—
761#67—108no—
762#67—108no—
763#67—108no—
764#67—204no—
765C2×Dic3—22no—
766C2×Dic3—22no—
767C2×Dic3—52no—
768C2×Dic3—52no—
769C2×Dic3—52no—
770C2×Dic3—108no—
771C2×Dic3—102no—
772C2×Dic3—102no—
773C2×Dic3—102no—
774C2×Dic3C23×D512yes—
775C2×Dic3C23×D512yes—
776D12—108no—
777C4×D3—108no—
778C4×D3—204no—
779C4×D3—204no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—22no—
783C22×C5—22no—
784C22×C5—22no—
785C22×C5—22no—
786C22×C5—34no—
787C22×C5—44no—
788C22×C5—44no—
789C22×C5—62no—
790C22×C5—62no—
791C22×C5—68no—
792C22×C5—62no—
793C22×C5—62no—
794C22×C5—62no—
795C22×C5—1216no—
796C22×C5—124no—
797C22×C5C2×D3×D412yes—
798C22×C5#100412yes—
799C22×C5#100412yes—
800C22×C5C24×D311yescharacteristic
801C2×D5—22no—
802C2×D5—22no—
803C2×D5—28no—
804C2×D5—22no—
805C2×D5—22no—
806C2×D5—22no—
807C2×D5—34no—
808C2×D5—416no—
809C2×D5—44no—
810C2×D5—62no—
811C2×D5—62no—
812C2×D5—68no—
813C2×D5—1216no—
814C2×D5C2×D3×D414yes—
815C4×C5—22no—
816C4×C5—62no—
817C4×C5—62no—
818Dic5—22no—
819Dic5—22no—
820Dic5—62no—
821Dic5—62no—
822Dic5—62no—
823C24—31no—
824C24—31no—
825C24—34no—
826C24—51no—
827C24—51no—
828C24—54no—
829C24—64no—
830C24—104no—
831C24—122no—
832C24—122no—
833C24—154no—
834C24—158no—
835C24—151no—
836C24—202no—
837C24—202no—
838C24—602no—
839C24—602no—
840C24C2×D3×D511yescharacteristic
841C24C2×D3×D511yescharacteristic
842C2×D4—34no—
843C2×D4—34no—
844C2×D4—42no—
845C2×D4—54no—
846C2×D4—54no—
847C2×D4—64no—
848C2×D4—104no—
849C2×D4—122no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—154no—
856C2×D4—154no—
857C2×D4—202no—
858C2×D4—304no—
859C2×D4—304no—
860C2×D4—3032no—
861C2×D4—3032no—
862C2×D4—304no—
863C2×D4—304no—
864C2×D4—304no—
865C2×D4—304no—
866C2×D4—602no—
867C2×D4C2×D3×D514yescomplemented
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—51no—
871C22×C4—51no—
872C22×C4—154no—
873C22×C4—154no—
874C22×C4—154no—
875C22×C4—151no—
876C22×C4—151no—
877C22×C4—151no—
878C22×C4—154no—
879C22×C4—304no—
880C22×C4—304no—
881C22×C4—602no—
882C22×C4—602no—
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—154no—
885C4⋊C4—154no—
886C4⋊C4—154no—
887C4⋊C4—154no—
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—34no—
891C22⋊C4—54no—
892C22⋊C4—54no—
893C22⋊C4—54no—
894C22⋊C4—154no—
895C22⋊C4—154no—
896C22⋊C4—154no—
897C22⋊C4—154no—
898C22⋊C4—154no—
899C22⋊C4—154no—
900C3×C5C2×#53411yescharacteristic, complemented, Hall
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—22no—
907C22×C3—44no—
908C22×C3—44no—
909C22×C3—54no—
910C22×C3—108no—
911C22×C3—102no—
912C22×C3—102no—
913C22×C3—102no—
914C22×C3—102no—
915C22×C3—102no—
916C22×C3—2016no—
917C22×C3—204no—
918C22×C3C2×D4×D512yes—
919C22×C3#414412yes—
920C22×C3#414412yes—
921C22×C3C24×D511yescharacteristic
922C2×D3—28no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—22no—
928C2×D3—416no—
929C2×D3—44no—
930C2×D3—54no—
931C2×D3—108no—
932C2×D3—102no—
933C2×D3—102no—
934C2×D3—2016no—
935C2×D3C2×D4×D514yes—
936C3×C4—22no—
937C3×C4—102no—
938C3×C4—102no—
939Dic3—22no—
940Dic3—22no—
941Dic3—102no—
942Dic3—102no—
943Dic3—102no—
944C2×C5—42no—
945C2×C5—42no—
946C2×C5—64no—
947C2×C5—122no—
948C2×C5#558914yescomplemented
949C2×C5C22×D3×D411yescharacteristic
950C2×C5C2×#100411yescharacteristic
951C2×C5C2×#100411yescharacteristic
952D5—24no—
953D5—42no—
954D5—64no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—34no—
962C23—32no—
963C23—32no—
964C23—54no—
965C23—52no—
966C23—52no—
967C23—68no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—108no—
974C23—102no—
975C23—102no—
976C23—102no—
977C23—102no—
978C23—102no—
979C23—124no—
980C23—124no—
981C23—1216no—
982C23—1516no—
983C23—154no—
984C23—152no—
985C23—204no—
986C23—204no—
987C23—2016no—
988C23—302no—
989C23—302no—
990C23—6016no—
991C23—604no—
992C23—604no—
993C23C22×D3×D512yes—
994C23C22×D3×D512yes—
995C23C22×D3×D511yescharacteristic
996D4—44no—
997D4—68no—
998D4—108no—
999D4—124no—
1000D4—204no—
1001D4—308no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—308no—
1006D4—308no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—52no—
1012C2×C4—52no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—102no—
1016C2×C4—102no—
1017C2×C4—152no—
1018C2×C4—152no—
1019C2×C4—152no—
1020C2×C4—308no—
1021C2×C4—308no—
1022C2×C4—302no—
1023C2×C4—302no—
1024C2×C4—302no—
1025C2×C4—604no—
1026C2×C4—604no—
1027C2×C4C22×D3×D512yes—
1028C2×C3—42no—
1029C2×C3—42no—
1030C2×C3—104no—
1031C2×C3—202no—
1032C2×C3#6592314yescomplemented
1033C2×C3C22×D4×D511yescharacteristic
1034C2×C3C2×#414411yescharacteristic
1035C2×C3C2×#414411yescharacteristic
1036D3—24no—
1037D3—42no—
1038D3—104no—
1039C5C2×#558911yescharacteristic, complemented, Sylow
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—34no—
1047C22—44no—
1048C22—44no—
1049C22—54no—
1050C22—68no—
1051C22—62no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—62no—
1056C22—108no—
1057C22—102no—
1058C22—102no—
1059C22—102no—
1060C22—102no—
1061C22—102no—
1062C22—1216no—
1063C22—124no—
1064C22—154no—
1065C22—2016no—
1066C22—204no—
1067C22—308no—
1068C22—302no—
1069C22—302no—
1070C22—6016no—
1071C22D3×D4×D512yes—
1072C22#9202512yes—
1073C22#9204912yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—62no—
1077C4—62no—
1078C4—102no—
1079C4—102no—
1080C4—302no—
1081C4—302no—
1082C4—302no—
1083C3C2×#6592311yescharacteristic, complemented, Sylow
1084C2—42no—
1085C2—42no—
1086C2—64no—
1087C2—104no—
1088C2—122no—
1089C2—202no—
1090C2—304no—
1091C2#1175502214yesdirect product factor
1092C2C2×D3×D4×D511yescharacteristic
1093C2C2×#9202511yescharacteristic
1094C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×D3×C22⋊D5C2semidirect
2. C22×D5×#67C2semidirect
3. C2×#91827C2semidirect
4. C2×C5×#937C2semidirect
5. C2×C3×#4083C2semidirect
6. C2×#91568C2semidirect
7. C2×#91563C2semidirect
8. C2×#91557C2semidirect
9. C2×#91555C2semidirect
10. C2×#91548C2semidirect
11. C2×#91533C2semidirect
12. #11755022C2direct (N × H)
13. C2×#91473C2semidirect
14. C2×#91461C2semidirect
15. C2×#91457C2semidirect
16. C2×#91414C2semidirect
18. C24×C5×D3C22semidirect
19. C24×C3×D5C22semidirect
21. C22×C3×C5×D4C22semidirect
22. C22×#1220C22semidirect
23. C22×#1220C22semidirect
24. C22×C4×D15C22semidirect
26. C22×C5×#67C22semidirect
28. C22×C3×C22⋊D5C22semidirect
30. C2×D3×C22⋊D5C22semidirect
32. C2×D5×#67C22semidirect
33. C22×#1203C22semidirect
34. C22×#1202C22semidirect
37. C22×#1201C22semidirect
38. C22×#1200C22semidirect
39. C22×D3×Dic5C22semidirect
40. C22×D5×Dic3C22semidirect
41. C2×#6719C22semidirect
42. C2×#6719C22semidirect
43. #91827C22semidirect
44. C2×C4⋊Dic15C22semidirect
45. C2×C5×#217C22semidirect
46. C5×#937C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
50. C3×#4083C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#685C22semidirect
53. #91568C22semidirect
54. #91563C22semidirect
55. #91557C22semidirect
56. #91555C22semidirect
57. #91548C22semidirect
58. C2×Dic3⋊Dic5C22semidirect
59. C2×#6669C22semidirect
60. C2×#6668C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×(C2×D3)⋊Dic5C22semidirect
63. C2×#6665C22semidirect
64. C2×#6665C22semidirect
65. #91533C22semidirect
66. #91473C22semidirect
67. #91461C22semidirect
68. #91457C22semidirect
69. #91414C22semidirect
78. C2×#4083D3semidirect
95. C23×C5×D3C23semidirect
101. C23×C3×D5C23semidirect
104. C22×D3×D5D4semidirect
107. C2×C3×C5×D4C23semidirect
111. C2×#1220C23semidirect
112. C2×#1220C23semidirect
117. C2×C4×D15C23semidirect
121. C2×C5×#67C23semidirect
127. C2×C3×C22⋊D5C23semidirect
133. C2×#1203C23semidirect
135. C2×#1202C23semidirect
141. C2×#1201C23semidirect
143. C2×#1200C23semidirect
145. C2×D3×Dic5C23semidirect
147. C2×D5×Dic3C23semidirect
148. #6719C23semidirect
149. #6719C23semidirect
150. C4⋊Dic15C23semidirect
151. C5×#217C23semidirect
152. C5×(C2×D3)⋊C4C23semidirect
153. C5×(C2×D3)⋊C4C23semidirect
154. C3×C22⋊Dic5C23semidirect
155. C3×#685C23semidirect
156. C3×#685C23semidirect
157. Dic3⋊Dic5C23semidirect
158. #6669C23semidirect
159. #6668C23semidirect
160. (C2×D3)⋊Dic5C23semidirect
161. (C2×D3)⋊Dic5C23semidirect
162. #6665C23semidirect
163. #6665C23semidirect
171. C2×#937D5semidirect
182. C24×D5C2×D3semidirect
185. C22×C5×D4C2×D3semidirect
195. C22×C22⋊D5C2×D3semidirect
212. C2×C22⋊Dic5C2×D3semidirect
216. #4083C2×D3semidirect
220. C2×#685C2×D3semidirect
221. C2×#685C2×D3semidirect
273. C2×D3×D5C2×D4semidirect
308. C24×D3C2×D5semidirect
311. C22×C3×D4C2×D5semidirect
321. C22×#67C2×D5semidirect
338. C2×#217C2×D5semidirect
342. #937C2×D5semidirect
346. C2×(C2×D3)⋊C4C2×D5semidirect
347. C2×(C2×D3)⋊C4C2×D5semidirect
376. C23×D5C22×D3semidirect
382. C2×C5×D4C22×D3semidirect
402. C2×C22⋊D5C22×D3semidirect
426. C22⋊Dic5C22×D3semidirect
429. #685C22×D3semidirect
430. #685C22×D3semidirect
512. C23×D3C22×D5semidirect
518. C2×C3×D4C22×D5semidirect
538. C2×#67C22×D5semidirect
562. #217C22×D5semidirect
565. (C2×D3)⋊C4C22×D5semidirect
566. (C2×D3)⋊C4C22×D5semidirect
662. C22×D4D3×D5semidirect
698. C2×C3×C5#534semidirect
867. C2×D4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
948. C2×C5#5589semidirect
1032. C2×C3#65923semidirect
1039. C5C2×#5589semidirect
1083. C3C2×#65923semidirect
1091. C2#11755022direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D3×C22⋊D52
C22×D5×#672
C2×#918272
C2×C5×#9372
C2×C3×#40832
C2×#915682
C2×#915632
C2×#915572
C2×#915552
C2×#915482
C2×#915332
#117550222
C2×#914732
C2×#914612
C2×#914572
C2×#914142
C2×#659233
C2×#55895